A Note on Limit Theorems for Multivariate Martingales
Uwe Küchler, Michael Sørensen, Uwe Küchler, Michael Sørensen · Bernoulli · 1999
Multivariate versions of the law of large numbers and the central limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic process models.To illustrate the usefulness of the results, we consider estimation for a multi-dimensional Gaussian di usion, where results on consistency and asymptotic normality of the maximum likelihood estimator are obtained in cases that were not covered by previously published limit theorems.The results are also applied to martingales of a di erent nature, which a r e t ypical of the problems occuring in connection with statistical inference for stochastic delay equations.